1. Carlos Varela Rensselaer Polytechnic Institute November 28, 2017
Logic Programming Prolog: Arithmetic, Equalities, Operators, I/O. (PLP 11) Databases: assert, retract. (CTM 9.6)
Carlos Varela
Rensselaer Polytechnic Institute
November 28, 2017
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2. Arithmetic Goals N>M N<M N=<M N>=M
N and M must be bound to numbers for these tests to succeed or fail.
X is 1+2 is used to assign numeric value of right-hand-side to variable in left-hand-side.
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3. Loop Revisited natural(1). natural(N) :- natural(M), N is M+1.
my_loop(N) :- N>0,
natural(I),
write(I), nl,
I=N, !.
my_loop(_).
Also called generate-and-test.
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4. = is not equal to == or =:=
X=Y X\=Y
test whether X and Y can be or cannot be unified.
X==Y X\==Y
test whether X and Y are currently co-bound, i.e., have been bound to, or share the same value.
X=:=Y X=\=Y
test arithmetic equality and inequality.
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5. More equalities X=@=Y X\=@=Y
test whether X and Y are structurally identical.
is weaker than == but stronger than =.
Examples:
false
true
false
true
true
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6. More on equalities X==Y  X=@=Y  X=Y but not the other way ().
If two terms are currently co-bound, they are structurally identical, and therefore they can unify.
Examples:
false
true
false
true
true
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7. Prolog Operators :- op(P,T,O)
declares an operator symbol O with precedence P and type T.
Example:
:- op(500,xfx,’has_color’)
a has_color red.
b has_color blue.
then:
?- b has_color C.
C = blue.
?- What has_color red.
What = a.
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8. Operator precedence/type
Precendence P is an integer: the larger the number, the less the precedence (ability to group).
Type T is one of: T
Position
Associativity
Examples
xfx
Infix
Non-associative is
xfy
Right-associative
, ;
yfx
Left-associative
+ - * / fx
Prefix ?- fy xf
Postfix yf
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9. Testing types atom(X) tests whether X is an atom, e.g., ‘foo’, bar.
integer(X)
tests whether X is an integer; it does not test for complex terms, e.g., integer(4/2) fails.
float(X)
tests whether X is a float; it matches exact type.
string(X)
tests whether X is a string, enclosed in `` … ``.
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10. Prolog Input seeing(X)
succeeds if X is (or can be) bound to current read port.
X = user is keyboard (standard input.)
see(X)
opens port for input file bound to X, and makes it current.
seen
closes current port for input file, and makes user current.
read(X)
reads Prolog type expression from current port, storing value in X.
end-of-file
is returned by read at <end-of-file>.
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11. Prolog Output telling(X)
succeeds if X is (or can be) bound to current output port.
X = user is screen (standard output.)
tell(X)
opens port for output file bound to X, and makes it current.
told
closes current output port, and reverses to screen output (makes user current.)
write(X)
writes Prolog expression bound to X into current output port. nl
new line (line feed).
tab(N)
writes N spaces to current output port.
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12. I/O Example browse(File) :- seeing(Old), /* save for later */
see(File), /* open this file */
repeat,
read(Data), /* read from File */
process(Data),
seen, /* close File */
see(Old), /* prev read source */
!. /* stop now */
process(end_of_file) :- !.
process(Data) :- write(Data), nl, fail.
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13. First-Class Terms Revisited
call(P)
Invoke predicate as a goal.
assert(P)
Adds predicate to database.
retract(P)
Removes predicate from database.
functor(T,F,A)
Succeeds if T is a term with functor F and arity A.
findall(F,P,L)
Returns a list L with all elements F
satisfying predicate P
clause(H,B)
Succeeds if the clause H :- B can be found in the database.
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14. Databases: assert and retract
Prolog enables direct modification of its knowledge base using assert and retract.
Let us consider a tic-tac-toe game:
We can represent a board with facts x(n) and o(n), for n in {1..9} corresponding to each player’s moves.
As a player (or the computer) moves, a fact is dynamically added to Prolog’s knowledge base. 1 2 3 4 5 6 7 8 9
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15. Databases: assert and retract
% main goal:
play :- clear, repeat, getmove, respond.
getmove :- repeat,
write('Please enter a move: '), read(X), empty(X),
assert(o(X)).
respond :- makemove, printboard, done.
makemove :- move(X), !, assert(x(X)).
makemove :- all_full.
clear :- retractall(x(_)), retractall(o(_)).
Human move
Computer move
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16. Tic-tac-toe: Strategy
The strategy is to first try to win, then try to block a win, then try to create a split (forced win in the next move), then try to prevent opponent from building three in a row, and creating a split, finally choose center, corners, and other empty squares. The order of the rules is key to implementing the strategy.
move(A) :- good(A), empty(A), !.
good(A) :- win(A).
good(A) :- block_win(A).
good(A) :- split(A).
good(A) :- strong_build(A).
good(A) :- weak_build(A).
good(5).
good(1). good(3). good(7). good(9).
good(2). good(4). good(6). good(8).
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17. Tic-tac-toe: Strategy(2)X
Moving x(8) produces a split: x(2) or x(7) wins in next move.
win(A) :- x(B), x(C), line(A,B,C).
block_win(A):- o(B), o(C), line(A,B,C).
split(A) :- x(B), x(C), different(B,C),
line(A,B,D), line(A,C,E), empty(D), empty(E).
strong_build(A) :- x(B), line(A,B,C), empty(C),
not(risky(C)).
weak_build(A) :- x(B), line(A,B,C), empty(C),
not(double_risky(C)).
risky(C) :- o(D), line(C,D,E), empty(E).
double_risky(C) :- o(D), o(E), different(D,E),
line(C,D,F), line(C,E,G), empty(F), empty(G).
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18. Databases in Oz: RelationClass
Oz supports dynamic database modifications using a RelationClass. The initial relation is defined as follows:
Rel = {New RelationClass init}
Once we have a relation instance, the following operations are possible:
{Rel assert(T)} adds tuple T to Rel.
{Rel assertall(Ts)} adds the list of tuples Ts to Rel.
{Rel query(X)} binds X to one of the tuples in Rel. X can be any partial value. If more than one tuple is compatible with X, then search can enumerate all of them.
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19. Databases in Oz: An examplec d e f
GraphRel = {New RelationClass init} {GraphRel assertall([edge(a b) edge(b c) edge(c d) edge(d e) edge(b e) edge(d f)])} proc {EdgeP A B} {GraphRel query(edge(A B))} end {Browse {Search.base.all proc {$ X} {EdgeP b X} end}} % displays all edges from node b: [c e]
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20. Databases in Oz: An example(2)
proc {Path X Y} choice X = Y [] Z in {EdgeP Z Y} {Path X Z} end {Browse {Search.base.all proc {$ X} {Path b X} end}} % displays all nodes with a path from node b: [b c e e f d]
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21. Exercises
The Prolog predicate my_loop/1 can succeed or fail as a goal. Explain why you may want a predicate to succeed, or fail depending on its expected calling context.
CTM Exercise (page 671). Do it both in Prolog and Oz.
PLP Exercise 11.7 (page 571), in Oz.
Develop a tic-tac-toe game in Oz.
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